Section 4: The Tax Multiplier and the Balanced Budget Multiplier

If an increase in government spending leads to an increase in total spending and GDP, then an increase in taxes must lead to a decrease in total spending and GDP, and vice versa. When the government raises taxes, private spending decreases. Keynes noted, however, that the decrease in overall spending from a tax increase is not as large as the increase in overall spending from the same amount of a government spending increase. The example in the next paragraph illustrates this.

The Tax Multiplier

Let’s say that taxes increase by $1,000. Therefore, people’s after-tax income (income available for consumption or savings) decreases by $1,000. If the MPC is 80%, then people would have only consumed $800 of this $1,000. Thus, total spending throughout the economy decreases by 5 (the multiplier) times $800 = $4,000. This $4,000 is 4 times the change in taxes.

Mathematically, we can prove that the tax multiplier is the negative of the spending multiplier minus 1. In the above example, the regular spending multiplier from the previous section is 5 and, therefore, the tax multiplier is -4. Thus,

The tax multiplier = – (the regular multiplier – 1)

In the above example:
The tax multiplier = – (5 – 1) = -4

The following applications provide further explanations of this concept.

Examples of How a Change in Taxes Affects GDP

Example 1
Problem: Let’s say that we are experiencing a recession and the government decreases taxes by $25 billion. Let’s also assume that the MPC equals .75. By how much will GDP increase?

Solution: Because the MPC equals .75, the regular (spending) multiplier equals 4, and the tax multiplier equals -3.
The spending multiplier = 1 / (1 minus .75) = 1 / .25 = 4. The tax multiplier equals 4 minus 1 with a negative sign: -(4 – 1) = -3.
To get the increase in GDP, we multiply the multiplier by the decrease in taxes:
Change in GDP = -3 x -$25 billion = +$75 billion.
This means that if GDP was $800 billion before the change, it will be $875 billion after the change.

Recessionary Gap

Example 2Problem: Let’s say that we are experiencing a recessionary gap of $360 billion. A recessionary gap is how much GDP needs to increase from the current GDP in order to achieve full employment. Also assume that the MPC equals .90. How much will the government have to decrease taxes in order to close the recessionary gap?

Solution: We know that the decrease in taxes times the tax multiplier equals the increase in GDP.
So: (the change in taxes) x (the multiplier) = the change in GDP.
So: (the change in taxes) x (-9) = $360 billion.
So: (the change in taxes) = $360 / (-9) = -$40 billion.
In other words, if the government decreases taxes by $40 billion, and the tax multiplier is -9, then GDP will increase by $360 billion. Since we need to add $360 billion to GDP to achieve full employment, we will have closed the recessionary gap.

Inflationary Gap

Example 3Problem: Let’s say that we are experiencing an inflationary gap of $200 billion. An inflationary gap is how much GDP needs to decrease from the current GDP in order to achieve full employment without causing inflation. Also assume that the MPC equals .80.

Solution: The change in taxes x the tax multiplier = the change in GDP.
So: (the change in taxes) x (-4) = -$200 billion.
So: (the change in taxes) = (-$200) / (-4)= +$50 billion.
In other words, if the government increases taxes by $50 billion, and the tax multiplier is -4, then GDP will decrease by $200 billion. Since we need to lower GDP by $200 billion to achieve full employment without inflation, we will have closed the inflationary gap.

The Balanced Budget Multiplier

When the government increases spending by a certain amount and it increases taxes by the same amount, then GDP will increase by that amount. The following example illustrates this.

Example 4Problem: Let’s say the government increases spending by $1,000 and also increases taxes by $1,000, and the MPC equals .8. By how much will GDP change?

Solution: The multiplier equals 5 and so the tax multiplier equals -4. Therefore, GDP will increase by $5,000 from the $1,000 additional government spending (5 times $1,000). And GDP will decrease by $4,000 from the additional $1,000 in taxes (-4 times $1,000). Thus, on balance, equilibrium income (GDP) will increase by $1,000 ($5,000 minus $4,000).

Therefore, when the government spends $1,000 and imposes taxes of $1,000, it balances its budget, while increasing equilibrium GDP by $1,000.

Thus, when the government changes spending and taxes by the same amount, then equilibrium income (GDP) changes by 1 times this amount. We say that

The balanced budget multiplier = 1.

The balanced budget multiplier implies that if the government increases spending and taxation by the same amount, then equilibrium national income (GDP) rises by this amount.

This balanced budget stimulation is possible, according to Keynes, because when the government receives $1,000, it spends it all. On the other hand, when private citizens receive $1,000, they spend only a fraction of it (in the above example, they spend 80%). They save the other fraction. Because savings, according to Keynes, is a “leakage” from the economy, the economy “loses” 20% in stimulation if private citizens spend it, compared to no loss (no savings) if the government spends it.

Do you agree with Keynes that it is possible to stimulate the economy by, for example, $1 trillion, simply by raising government spending and taxes by $1 trillion?

For a video explanation of additional examples involving the Keynesian multiplier, please watch:

2 Comments

Nikhil Gautam
on October 8, 2017 at 1:40 pm

Well it’s great to know that , multiplier concepts become easier by given your examples . But still I have a question ” what about the value of ‘ Balance budget multiplier ‘ when tax is in form of linear function as T= Ta+tY.
Please give me answer, and vanish my confusion…